Local Quantum Field Theory of Possible Violation of the Pauli Principle

We generalize to a local relativistic quantum field theory a proposal of Ignatiev and Kuzmin for a single oscillator which has small violation of the Pauli principle and thus provide a theoretical framework which, for the first time, allows quantitative tests of the Pauli principle. Our theory provides a continuous interpolation between fully hindered parafermi statistics of order 2 ($\beta =0\mathrm{}$), which is equivalent to Fermi statistics, and ordinary parafermi statistics of order 2 ($\beta =1\mathrm{}$). We suggest two types of experiments which can place bounds on $\beta$.